Uncertainty Quantification and Sensitivity Analysis of Transonic Aerodynamics with Geometric Uncertainty

Airfoil geometric uncertainty can generate aerodynamic characteristics fluctuations. Uncertainty quantification is applied to compute its impact on the aerodynamic characteristics. In addition, the contribution of each uncertainty variable to aerodynamic characteristics should be computed by the uncertainty sensitivity analysis. In the paper, Sobol’s analysis is used for uncertainty sensitivity analysis and a nonintrusive polynomial chaos method is used for uncertainty quantification and Sobol’s analysis. It is difficult to describe geometric uncertainty because it needs a lot of input parameters. In order to alleviate the contradiction between the variable dimension and computational cost, a principal component analysis is introduced to describe geometric uncertainty of airfoil. Through this technique, the number of input uncertainty variables can be reduced and typical global deformation modes can be obtained. By uncertainty quantification, we can learn that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region, which is the main reason that transonic drag is sensitive to the geometric uncertainty. The sensitivity analysis shows that the model can be simplified by eliminating unimportant geometric modes. Moreover, which are the most important geometric modes to transonic aerodynamics can be learnt. This is very helpful for airfoil design.

Unsteady transonic aerodynamics during wing flutter

Unsteady pressure distributions of a two-dimensional super-critical wing while it was fluttering were measured in the transonic flow regime. The results were compared with those by the Navier-Stokes code which includes wind-tunnel wall effects. Although there were discrepancies between the experimental results and the analytical model for the pressure phase delay distribution, no disagreements were observed for the pitching first harmonics provided that there was no large flow separation. In the tests, the flutter was forced to be suppressed soon after its onset before it reached a limit cycle oscillation (LCO) where the amplitude of the pitching angle was supposed to be over 2 degrees.